Question

How do you write $0.285$ as a fraction in simplest terms?

Answer 1

Hint: In this question convert a decimal number to a fraction. First we will remove all the decimal numbers by dividing and multiplying the decimal number by $10$ and then we will simplify the fraction to get the simplest form of the fraction.

Complete step by step answer:

For converting decimal number to fraction, we will follow the given steps:

First step: the decimal number is rewrite in the form of fraction. The decimal number comes in the numerator and in the denominator write $1$.

Second step: multiply the both numerator and denominator with $10$ and it is repeated up to when the decimal point is reached in the end.(and also we calculate direct as: if there is one digit after decimal point then multiply both numerator and denominator with ten, if there is two digit after decimal point then multiply both numerator and denominator with hundred and if there is three digit after decimal point then we multiply both numerator and denominator with thousand.)

Third step: then calculate the simplest form from fraction.

In the question, the decimal number is given as $0.285$.

For converting in fraction form we want to write $1$ in the denominator. And

Then,

The fraction form is given as below.

$ \Rightarrow \dfrac{{0.285}}{1}$

In the fraction form, we want to multiply with $10$in both numerator and denominator.

Then the new fraction form is come as below:

$ \Rightarrow \dfrac{{2.85}}{{10}}$

Now we will check that the decimal point is reached in the end or not, if not then multiply again by $10$in both numerator and denominator.

Then, the new form comes as below.

$ \Rightarrow \dfrac{{28.5}}{{100}}$

Again, repeat the step for check of decimal point, it is reached in the end or not, if not then multiply with $10$in both numerator and denominator.

Then,

$ \Rightarrow \dfrac{{285}}{{1000}}$

Now, we check that the decimal point is reached in the end, if the answer is yes then come to the next step and express in simplest form.

Then,

In the form of fraction, $5$ is common in both numerator and denominator. Then we divided both with$5$.

Then,

$ \Rightarrow \dfrac{\dfrac{285}{5}}{\dfrac{1000}{5}}$

After simplification, we will get

$\therefore \dfrac{{57}}{{200}}$

Therefore, the fraction of a decimal number $0.285$ is $\dfrac{{57}}{{200}}$.

Note: As we know that if a decimal number is given and want to convert its fraction form then we assume the $1$ in the denominator. And multiply both numerator and denominator with$10$, it is repeated up to when the decimal number is reached in the end.